Growth

In Optique the concept of growth (noted γ ) is associated with the report/ratio of a size of the Objet to its equivalent for the image of this object through a optical Système. It is a Grandeur without dimension, which makes it possible to connect:

  • sizes of the object and the image: transverse growth,
  • the angles under which are an object and its image: angular growth,
  • respective positions of the object and the image on the optical axis: longitudinal growth.

That is to say AB the object and A' B' the image of this object given by a convergent thin lens.

There is then the following relation:

γ = \ overline {A' B'} \ over \ overline {AB} = \ overline {OA'} \ over \ overline {OA}

\overline{OA} : the distance between the point has and the optical center O of the lens;

\overline{OA'} : the distance between a' point (image of has by the lens) and the optical center of the lens;

\overline{AB} : the height of object AB;

\overline{A'B'} : the height of the image A' B';

Note: The growth is expressed without unit.

Properties

If γ > the 0 then image is right (it the same direction has as the object)

If γ < the 0 then image is reversed (opposite direction)

If |γ| > 1 then the image is larger than the object

If |γ| < 1 then the image is smaller than the object

If one considers a convergent thin lens of focal distance f' and an object AB placed at D = 2*f' of the optical center of this lens then the image A' B' will appear after the lens at the same distance D and one will have for the growth: γ = - 1. An application of this property is the Méthode of Silbermann in Focométrie.

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